The use of a procedure of this kind for filling packaging is already known; these packagings do not consist entirely of paper or cardboard, but incorporate an inner layer of plastic film. The inner layer or the inner bag of plastic film is usually fixed to the adjacent layer of paper or cardboard by means of adhesive. Fixing the plastic inner bag to the outer bag is inconvenient if this is done only at one end of the package in a small area. If this is done, fragments of plastic remain on the outer packaging portion that consists of paper or cardboard after the loose inside bag has been separated, and this renders recycling of those layers of the packaging that are made of paper or cardboard considerably more difficult.